The experimental and numerical study both generation and transmission terahertz pulse in a nonlinear crystal partially filling the rectangular metallic waveguide cross-section is presented. LiNbO3 and DAST crystals have been studied since they have a high-quality factor (FOM) and optical rectification in them is the most promising method for generating an extremely strong terahertz field. Experimentally and numerically has been shown that, depending on the thickness and permittivity of a nonlinear crystal, a broadband terahertz pulse can propagate with low absorption in the form of the fundamental H10 mode or a linear superposition of Hno modes.